Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
Welcome to our Physics lesson on Galilean Transformations of Velocity, this is the second lesson of our suite of physics lessons covering the topic of Classical Principle of Relativity, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Let's wait until a short time interval Δt elapses after the particle have initially been at the position P, as shown in the figure discussed in the previous paragraph. Obviously, the particles coordinates have changed from x to x + Δx, from y to y + Δy and from z to z + Δz in the system S and from x' to x' + Δx', from y' to y' + Δy' and from z' to z' + Δz' in the system S'.
Subtracting side by side the corresponding quantities and considering the Galilean Transformations obtained earlier, we get
Dividing side by side all the above equations by Δt, we obtain:
The limit of the above equations for Δt → 0 give the corresponding velocities. Thus, we obtain
These formulae represent the three Galilean Transformations for Velocity. As we see, not only the position is relative; the velocity can be relative as well. Velocity depends on where do we make the observation (in S or S').
The above formulae represent the velocity in the system S' in respect to the system S. We can also express the inverse relationship between velocity components, i.e. the velocity in the system S in respect to values in the system S'. Thus, we have
An athlete running at 28.8 km/h throws a javelin in the forward direction. If the velocity of javelin relative to the athlete is 30 m/s, what is the horizontal component of javelin's velocity when it pins on the ground? Ignore the air resistance.
Since air resistance is not considered, we assume the horizontal component of all velocities as constant. When we consider a reference frame connected to the ground (at rest), we obtain for the horizontal velocity vx at which the javelin pins on the ground as
where V is the running velocity of the athlete and vx' is the javelin's velocity relative to the athlete.
Thus, giving that
we obtain for the horizontal component of velocity by which the javelin hits the ground:
As for the vertical component of javelin's velocity, it is not affected by what reference frame we choose, because the initial velocities (running velocity and javelin's throwing one) are both horizontal. Likewise, there is no change in the z-component of velocity (all are zero) regardless the reference frame we choose.
You have reached the end of Physics lesson 18.2.2 Galilean Transformations of Velocity. There are 5 lessons in this physics tutorial covering Classical Principle of Relativity, you can access all the lessons from this tutorial below.
Enjoy the "Galilean Transformations of Velocity" physics lesson? People who liked the "Classical Principle of Relativity lesson found the following resources useful:
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Physics lesson "Classical Principle of Relativity" useful. If you did it would be great if you could spare the time to rate this physics lesson (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.